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First-principles calculation of dynamical properties of insulators in finite electric fields and anomalous Hall conductivity of ferromagnets based on Berry phase approach

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Title
First-principles calculation of dynamical properties of insulators in finite electric fields and anomalous Hall conductivity of ferromagnets based on Berry phase approach
Name (ID = NAME001); (type = personal)
NamePart (type = family)
Wang
NamePart (type = given)
Xinjie
DisplayForm
Xinjie Wang
Role
RoleTerm (authority = RULIB)
author
Name (ID = NAME002); (type = personal)
NamePart (type = family)
Vanderbilt
NamePart (type = given)
David
Affiliation
Advisory Committee
DisplayForm
David Vanderbilt
Role
RoleTerm (authority = RULIB)
chair
Name (ID = NAME003); (type = personal)
NamePart (type = family)
Croft
NamePart (type = given)
Mark
Affiliation
Advisory Committee
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Mark Croft
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RoleTerm (authority = RULIB)
internal member
Name (ID = NAME004); (type = personal)
NamePart (type = family)
Andrei
NamePart (type = given)
Natan
Affiliation
Advisory Committee
DisplayForm
Natan Andrei
Role
RoleTerm (authority = RULIB)
internal member
Name (ID = NAME005); (type = personal)
NamePart (type = family)
Shapiro
NamePart (type = given)
Joel
Affiliation
Advisory Committee
DisplayForm
Joel Shapiro
Role
RoleTerm (authority = RULIB)
internal member
Name (ID = NAME006); (type = personal)
NamePart (type = family)
Hamann
NamePart (type = given)
Donald
Affiliation
Advisory Committee
DisplayForm
Donald Hamann
Role
RoleTerm (authority = RULIB)
outside member
Name (ID = NAME007); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (ID = NAME008); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2007
DateOther (qualifier = exact); (type = degree)
2007
Language
LanguageTerm
English
PhysicalDescription
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electronic
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application/pdf
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text/xml
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xiv, 139 pages
Abstract
We present first-principles methods for calculating two distinct types of physical quantities within the framework of density functional theory: the response properties of an insulator to finite electric fields, and the anomalous Hall conductivity of a ferromagnet. Both of the methods are closely related to the same ingredient, namely the Berry phase, a
geometric phase acquired by a quantum system transporting in parameter space. We develop
gauge-invariant formulations in which the random phases of Bloch functions produced by numerical subroutines are irrelevant.
First, we provide linear-response methods for calculating phonon frequencies, Born effective charge tensors and dielectric tensors for insulators in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded with respect to both small atomic displacements and electric fields within the framework of density-functional perturbation theory. The linear responses of
field-polarized Bloch functions to atomic displacements and electric fields are obtained by minimizing the second-order derivatives of the
total-energy functional. The desired second-order tensors are then constructed from these optimized first-order field-polarized Bloch functions.
Next, an efficient first-principles approach for computing the anomalous Hall conductivity is described. The intrinsic anomalous Hall conductivity in ferromagnets depends on subtle spin-orbit-induced effects in the electronic structure, and recent {it ab-initio} studies found that it was necessary to sample the Brillouin zone at millions of k-points to converge the calculation.
We start out by performing a conventional
electronic-structure calculation including spin-orbit coupling on a uniform and relatively coarse k-point mesh. From the resulting Bloch states, maximally localized Wannier functions are constructed which reproduce the {it ab-initio}
states up to the Fermi level. With inexpensive Fourier and unitary transformations the quantities of interest are interpolated onto a dense k-point mesh and used to evaluate the anomalous Hall conductivity as a Brillouin-zone integral. The present scheme, which also avoids the cumbersome summation over all unoccupied states in the Kubo formula, is applied to bcc Fe, giving excellent agreement with conventional, less efficient first-principles calculations.
Finally, we consider another {it ab-initio} approach for computing the anomalous Hall conductivity based on Haldane's Fermi-surface formulation. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi surface sheets with theslice by standard contour methods, organize these into a set of closed loops, and compute the Berry phase of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 134-138).
Subject (ID = SUBJ1); (authority = RUETD)
Topic
Physics and Astronomy
Subject (ID = SUBJ2); (authority = ETD-LCSH)
Topic
Electric conductivity--Measurement
Subject (ID = SUBJ3); (authority = ETD-LCSH)
Topic
Hall effect
Subject (ID = SUBJ4); (authority = ETD-LCSH)
Topic
Geometric quantum phases
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16791
Identifier
ETD_395
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3QJ7HQD
Genre (authority = ExL-Esploro)
ETD doctoral
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Xinjie Wang
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Rutgers University. Graduate School - New Brunswick
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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